Predicate Circumscription Convention: “minimize P without changing anything else in the model.” I.e., it keeps everything else fixed. Variable Circumscription Convention: “minimize P and let certain other designated predicates vary.” I.e., allow other predicates’ extent to grow, if it minimizes P. Variable Circumscription Definition: Circumscribe P in KB, allowing Z to vary: CIRC(KB;P;Z) = KB(P,Z) ? ? (?P*Z*. KB(P*,Z*) ? (P* ? P)) In our example, variable circumscription will enable us to make the extent of ab smaller at the expense of making the extent of ontable larger.
“Variable” Circumscription